Magnetic spin equilibrium (${\Omega }_{\ast }\sim {\Omega }_K(r_m)$)

The spin at which the net material and magnetic torque on an accreting star vanishes. The corotation radius is typically comparable to the magnetospheric truncation radius, but the precise torque balance depends on the coupling and any outflow.

With magnetic spin equilibrium at the magnetospheric truncation radius, $T\propto R_M^{3/2}{M}^{-1/2}\propto B_{\ast }^{6/7}{R}_{\ast }^{18/7}{\dot{M}}^{-3/7}$ at fixed mass. Inserting the surface accretion Eddington rate changes the radius power to $15/7$. The relation assumes the boundary remains outside the star; very weak fields instead encounter surface-accretion and mass-shedding limits.